Angular momentum in spin-phonon processes

Quantum theory of spin relaxation in the elastic environment is revised with account of the concept of a phonon spin recently introduced by Zhang and Niu (PRL 2014). Similar to the case of the electromagnetic field, the division of the angular momentum associated with elastic deformations into the orbital part and the part due to phonon spins proves to be useful for the analysis of the balance of the angular momentum. Such analysis sheds important light on microscopic processes leading to the Einstein - de Haas effect.